Distributive Property in Algebra

Distributive property is one of the most important rules in algebra. It allows you to simplify algebraic expressions by distributing multiplication over addition and subtraction.

Distributive property states that multiplying a sum by a number gives the same result as multiplying each addend separately and then adding the products.

In this article, we will discuss distributive property in algebra.

Distributive Property with Multiplication

Distributive property can be expressed in the following way for multiplication:

a(b + c) = ab + ac

This means that multiplying a sum in parentheses by a value outside the parentheses is the same as multiplying each part of the sum individually and then adding the results.

Example

3(x + 5) = 3x + 15

To show this:

3(x + 5)

= 3x + 3(5)

= 3x + 15

So the distributive property allowed us to distribute the 3 to each part of the sum x + 5.

Distributive Property with Division

Distributive property works similarly with division:

a/(b + c) = a/b + a/c

Example

6/(2 + 3)

= 6/2 + 6/3

= 3 + 2

= 5

So the distributive property allowed us to divide 6 separately by the 2 and 3 in the denominator.

Examples Using the Distributive Property

Example

4(x – 2)

4(x – 2) = 4x – 8

Example

(x + 4)/5

(x + 4)/5 = x/5 + 4/5

Example

5(x – 3y)

5(x – 3y) = 5x – 15y

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